Entropy Based Student’s t-Process Dynamical Model

Abstract

Volatility, which represents the magnitude of fluctuating asset prices or returns, is used in the problems of finance to design optimal asset allocations and to calculate the price of derivatives. Since volatility is unobservable, it is identified and estimated by latent variable models known as volatility fluctuation models. Almost all conventional volatility fluctuation models are linear time-series models and thus are difficult to capture nonlinear and/or non-Gaussian properties of volatility dynamics. In this study, we propose an entropy based Student’s t-process Dynamical model (ETPDM) as a volatility fluctuation model combined with both nonlinear dynamics and non-Gaussian noise. The ETPDM estimates its latent variables and intrinsic parameters by a robust particle filtering based on a generalized H-theorem for a relative entropy. To test the performance of the ETPDM, we implement numerical experiments for financial time-series and confirm the robustness for a small number of particles by comparing with the conventional particle filtering.

An adaptive multivariate Student's t‐process recursive method for hypersonic glide vehicle trajectory prediction

“…Unfortunately, because the Student's t-distribution has different properties from the Gaussian distribution, it is difficult to predict HGV trajectories directly using the Student's t-process regression. Meanwhile, the choice of initial values of Student's t-process regression parameters can seriously affect the prediction results [31].…”

“…ij and π ij have the functional form of(31). Divide each element in Π by π 21 , and the result is as follows.…”

Time Series Modelling

“…Roughly one-half of the contributed articles deal with real-valued time series (thus having a continuous range). In Nono et al [ 3 ], an entropy-based Student’s t -process dynamical model is proposed for dealing with non-Gaussian and non-linear univariate time series, whose relevance is demonstrated by an application to financial time series. The paper by Davidescu et al [ 4 ] is centered around the time series of Romanian unemployment rates, which serves as the base for comparing the forecast performance of several well-established time series models.…”